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For example, the minimum spanning tree of the graph associated with an instance of the Euclidean TSP is a Euclidean minimum spanning tree, and so can be computed in expected O(n log n) time for n points (considerably less than the number of edges). This enables the simple 2-approximation algorithm for TSP with triangle inequality above to ...
The Concorde TSP Solver is a program for solving the travelling salesman problem. It was written by David Applegate , Robert E. Bixby , Vašek Chvátal , and William J. Cook , in ANSI C , and is freely available for academic use.
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
In combinatorial optimization, the set TSP, also known as the generalized TSP, group TSP, One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the traveling salesman problem (TSP), whereby it is required to find a shortest tour in a graph which visits all specified subsets of the vertices of a graph.
The Held–Karp algorithm, also called the Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman [1] and by Held and Karp [2] to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to ...
Relocation is the process of assigning load addresses for position-dependent code and data of a program and adjusting the code and data to reflect the assigned addresses. [1] [2] Prior to the advent of multiprocess systems, and still in many embedded systems, the addresses for objects are absolute starting at a known location, often zero.
The multi-fragment (MF) algorithm is a heuristic or approximation algorithm for the travelling salesman problem (TSP) (and related problems). This algorithm is also sometimes called the "greedy algorithm" for the TSP.
Since the traveling salesman problem is NP-hard, the job-shop problem with sequence-dependent setup is clearly also NP-hard since the TSP is a special case of the JSP with a single job (the cities are the machines and the salesman is the job). [citation needed]